Moving data from HTC Desire HD to Samsung Galaxy Note IISupport

Hi,
Could someone give me few tips how to transfer various data from that old HTC? I don't mean stuff like music/videos/ebooks/photos but something like game saves/progress (mainly Angry Birds series but few less popular ones too), contacts, SMS (used "SMS Backup & Restore in the past but only Desire HD to Desire HD). Some kind of syncing with Google account or specially designated application? Unfortunately I must discard option with SIM card backup because the new microSIM would be completely clean with no data from the old full sized card.

BTW: I'm mainly concentrated on the first issue because loosing that progress would be quite painful.